Importance Sampling for Multiscale Diffusions

Details Importance Sampling for Multiscale Diffusions Importance Sampling for Multiscale Diffusions

2011-07-27

arxiv.org/abs/1107.5448v1

SIAM Journal on Multiscale Modeling and Simulation , Vol. 12, No. 1, 2012, pp. 1-27

Mathematics

Probability

Scientific paper

10.1137/110842545

We construct importance sampling schemes for stochastic differential equations with small noise and fast oscillating coefficients. Standard Monte Carlo methods perform poorly for these problems in the small noise limit. With multiscale processes there are additional complications, and indeed the straightforward adaptation of methods for standard small noise diffusions will not produce efficient schemes. Using the subsolution approach we construct schemes and identify conditions under which the schemes will be asymptotically optimal. Examples and simulation results are provided.

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